While finding an optimal OCT set is hard, recent implementations [1]} of a heuristic ensemble alongside algorithms from  [2]}, [3]} alleviate concerns that finding a good OCT decomposition creates a barrier to usability. For the sake of testing the efficacy of structural rounding, the OCT sets do not need to be optimal. We make use of a simple algorithm to find OCT sets: find two disjoint maximal independent sets and let the remaining vertices be our OCT set. See Section REF  for more details on how we carry out this process.
